Factor the following trinomials completely.z2−11z+30z^2-11z+30

( z − 5 ) ( z − 6 ) \left(z-5\right)\left(z-6\right) ( z − 5 ) ( z − 6 )

Factor the following trinomials completely. z 2 − 11 z + 30 z^2-11z+30

Since this polynomial has a leading term of just z squared, we're going to use the method that we learned recently to factor it where we ask ourselves what are two numbers that multiply to my c value and add to my b value. So let's start by listing some factor pairs of 30. We've got one and thirty, as well as two and fifteen, three and ten, and five and six. Now do any of these sum to 11? Yes. Five plus six equals 11. But we're not looking for positive 11, we're actually looking for negative 11. So instead we're going to use the factors negative five and negative six, which sum to negative 11 and still have a product of positive 30. So this means I can factor this polynomial as z minus five times z minus six, and this is our final answer.

Factor the following trinomials completely. z 2 − 11 z + 30 z^2-11z+30

( z − 5 ) ( z − 6 ) \left(z-5\right)\left(z-6\right) ( z − 5 ) ( z − 6 )

( z + 5 ) ( z − 6 ) \left(z+5\right)\left(z-6\right) ( z + 5 ) ( z − 6 )

( z − 3 ) ( z − 10 ) \left(z-3\right)\left(z-10\right) ( z − 3 ) ( z − 10 )

( z + 5 ) ( z + 6 ) \left(z+5\right)\left(z+6\right) ( z + 5 ) ( z + 6 )

7. Factoring

Factoring Trinomials of the Form x² + bx + c

Beginning & Intermediate Algebra

7. Factoring

Factoring Trinomials of the Form x² + bx + c

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Multiple Choice

Factor the following trinomials completely.
$z^{2} - 11 z + 30$

$\left(z+5\right)\left(z-6\right)$

$\left(z-3\right)\left(z-10\right)$

$\left(z+5\right)\left(z+6\right)$

$\left(z-5\right)\left(z-6\right)$

Verified step by step guidance

Identify the trinomial to factor: $z^2 - 11z + 30$.

Look for two numbers that multiply to the constant term \$30$ and add up to the coefficient of the middle term, which is $-11$.

List the factor pairs of \$30$: $(1, 30)$, $(2, 15)$, $(3, 10)$, and $(5, 6)$, and consider their signs to sum to $-11$.

Since the middle term is negative and the constant is positive, both numbers must be negative. Check which pair of negative numbers multiply to \$30$ and add to $-11$: $-5$ and $-6$.

Write the factored form using these numbers: $(z - 5)(z - 6)$.

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